Sample Size and Standard Error of a Single ROC is based on the calculation of the Standard Error (SE) from θ,
as described by Hanley and McNeil (see references). The sample size is calculated by iterative approximation until
the required Standard Error is obtained. The confidence interval is θ±z(SE)

The sample size table for a single ROC in the next panel is based upon the following arguments

The Standard Error (SE) from a nominated θ is calculated so that its one tail 95% confidence interval reaches but does
not overlap the null value of 0.5.

As the one tail z value for 95% confidence interval is 1.65, θ-1.65SE=0.5, so SE = (θ-0.5) / 1.65

Sample size is then calculated using θ and SE

This sample size is the number of cases in each of the two groups (Outcome Positive (O+) and Outcome Negative (O-), so the total
sample size is twice that presented.

This sample size is the minimum required to obtain a significant θ. In most cases, where a precise θ is required, or
comparison between multiple θ is intended, a narrower SE and therefore a larger sample size is used.

Sample size and power calculations for comparing two ROCs is also based on the formula described by Hanley and McNeil
(see references). It assumes that θ is a population measurement and approximately normally distributed, so that
the difference is Diff=θ1-θ2, and the Standard Error of the difference is the root sum
square of the individual Standard Errors SEdiff = sqrt(θ12+θ22)

The sample size calculated is for the one tail model. Those requiring a two tail model can use the same calculations but the
Type I Error value (α) is halved.

The sample size is for the total number of cases (number of Outcome Positive + number of Outcome Negative) in each of
the two ROCs.

Instead of using the z=diff/SEDiff or the 95% confidence interval of the difference to assess statistical
significance, the power calculation can also be used to see if the data contains sufficient power to satisfy the user's
requirement. Commonly a power in the data exceeding 0.8 for a nominated α of 0.05 is taken as a statistically
significant difference.

The table in the next panels provides sample size requirements for 3 levels of power (0.8, 0.9, 0.95), 3 levels of α
(0.1, 0.05, 0.01), and difference between two θ values from 0.5 upwards at 0.02 intervals.

Table on this page provides minimal sample size required, for each of the two groups (Outcome Positive and Outcome Negative),
to obtain a statistically significant Receiver Operator Characteristics. Calculation is based on θ and its Standard Error (SE),
the formula is as follows

This calculation assumes that the researcher will onbtain equal sample size for Outcome Positive and Outcome Negative groups

The sample size is for each group, so the total sample size is twice that in the table

The sample size calculated is for the minimum number of cases required to achieve a statistically significant value,
that the one tail 95% confidence does not overlap the null (0.5) value. In most research projects, a more
precise (narrower) Standard Error is desirable, so the sample size will need to be bigger.

Only θ > 0.5 is calculated. A θ=0.5 has no predictive value at all, and θ < 0.5 predicts in the
wrong direction.

θ

SSiz

θ

SSiz

θ

SSiz

θ

SSiz

θ

SSiz

θ

SSiz

θ

SSiz

θ

SSiz

θ

SSiz

θ

SSiz

0.51

1000

0.52

1000

0.53

503

0.54

282

0.55

180

0.56

125

0.57

91

0.58

70

0.59

55

0.6

44

0.61

36

0.62

30

0.63

26

0.64

22

0.65

19

0.66

17

0.67

15

0.68

13

0.69

11

0.7

10

0.71

9

0.72

8

0.73

7

0.74

7

0.75

6

0.76

6

0.77

5

0.78

5

0.79

4

0.8

4

0.81

4

0.82

3

0.83

3

0.84

3

0.85

3

0.86

3

0.87

3

0.88

3

0.89

3

0.9

3

0.91

3

0.92

3

0.93

3

0.94

3

0.95

3

0.96

3

0.97

3

0.98

3

0.99

3

α=Probability of Type I Error, β=Probability of Type II Error
θ1 and θ2 are values of the two ROCs being compared
Sample Size is total of both groups (outcome Positive + Outcome Negative) for each of the two ROCs, for θ1
and the same number of cases for θ2Sample size is for a One Tail model. For two tail model, use the same calculation, but halve the &alpha value

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

0.50

0.52

3756

5151

8362

5472

7134

10844

7133

9015

13137

0.50

0.54

938

1287

2089

1366

1782

2709

1781

2251

3281

0.50

0.56

416

571

928

606

790

1202

790

998

1455

0.50

0.58

234

321

521

340

443

675

443

560

817

0.50

0.60

149

205

333

217

283

431

282

357

521

0.50

0.62

103

142

231

150

196

298

195

247

360

0.50

0.64

76

104

169

110

143

218

142

180

263

0.50

0.66

58

79

129

83

109

166

108

137

201

0.50

0.68

45

62

102

65

86

131

85

107

157

0.50

0.70

37

50

82

53

69

105

68

86

127

0.50

0.72

30

41

67

43

56

86

56

71

104

0.50

0.74

25

35

56

36

47

72

46

59

87

0.50

0.76

21

29

48

30

40

61

39

50

73

0.50

0.78

18

25

41

26

34

52

33

42

62

0.50

0.80

16

22

36

22

29

45

28

36

54

0.50

0.82

14

19

31

19

25

39

25

31

47

0.50

0.84

12

17

27

17

22

34

21

27

41

0.50

0.86

11

15

24

15

20

30

19

24

36

0.50

0.88

10

13

22

13

17

27

17

21

32

0.50

0.90

9

12

19

12

15

24

15

19

28

0.50

0.92

8

11

17

10

14

22

13

17

25

0.50

0.94

7

10

16

9

12

19

12

15

23

0.50

0.96

6

9

14

8

11

18

10

14

20

0.50

0.98

6

8

13

8

10

16

9

12

18

0.52

0.54

3745

5137

8341

5456

7114

10815

7111

8988

13101

0.52

0.56

935

1283

2083

1361

1775

2700

1773

2242

3269

0.52

0.58

415

569

924

603

787

1197

785

993

1449

0.52

0.60

233

319

519

338

441

672

440

556

812

0.52

0.62

148

204

331

215

281

428

280

354

518

0.52

0.64

103

141

229

149

194

296

193

245

358

0.52

0.66

75

103

168

109

142

217

141

179

261

0.52

0.68

57

79

128

83

108

165

107

136

199

0.52

0.70

45

62

101

65

85

130

84

106

156

0.52

0.72

36

50

81

52

68

104

67

85

125

0.52

0.74

30

41

67

43

56

86

55

70

103

0.52

0.76

25

34

56

35

46

71

46

58

86

0.52

0.78

21

29

47

30

39

60

38

49

72

0.52

0.80

18

25

41

25

33

52

33

42

62

0.52

0.82

16

21

35

22

29

44

28

36

53

0.52

0.84

14

19

31

19

25

39

24

31

46

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

0.52

0.86

12

16

27

17

22

34

21

27

40

0.52

0.88

11

15

24

15

19

30

18

24

35

0.52

0.90

9

13

21

13

17

27

16

21

31

0.52

0.92

8

12

19

11

15

24

14

19

28

0.52

0.94

8

10

17

10

14

21

13

16

25

0.52

0.96

7

9

16

9

12

19

11

15

22

0.52

0.98

6

9

14

8

11

17

10

13

20

0.54

0.56

3720

5104

8288

5419

7066

10744

7062

8927

13013

0.54

0.58

928

1273

2068

1350

1762

2680

1759

2224

3244

0.54

0.60

411

565

917

598

780

1188

778

984

1437

0.54

0.62

231

317

515

335

437

666

435

551

805

0.54

0.64

147

202

329

213

278

424

277

351

513

0.54

0.66

102

140

227

147

192

293

191

242

354

0.54

0.68

74

102

166

107

140

214

139

176

258

0.54

0.70

57

78

127

81

107

163

105

134

196

0.54

0.72

44

61

100

64

84

128

82

105

154

0.54

0.74

36

49

80

51

67

103

66

84

124

0.54

0.76

29

40

66

42

55

84

54

69

101

0.54

0.78

24

34

55

35

46

70

45

57

84

0.54

0.80

21

29

47

29

39

59

37

48

71

0.54

0.82

18

24

40

25

33

51

32

41

60

0.54

0.84

15

21

35

21

28

44

27

35

52

0.54

0.86

13

18

30

19

25

38

24

30

45

0.54

0.88

12

16

27

16

21

33

20

26

39

0.54

0.90

10

14

24

14

19

29

18

23

35

0.54

0.92

9

13

21

13

17

26

16

20

31

0.54

0.94

8

11

19

11

15

23

14

18

27

0.54

0.96

7

10

17

10

13

21

12

16

24

0.54

0.98

7

9

15

9

12

19

11

14

22

0.56

0.58

3681

5050

8202

5360

6990

10631

6984

8830

12875

0.56

0.60

917

1259

2046

1334

1741

2650

1738

2198

3207

0.56

0.62

406

558

907

590

770

1173

768

972

1419

0.56

0.64

228

313

509

330

431

657

429

543

794

0.56

0.66

145

199

324

210

274

419

272

345

505

0.56

0.68

100

138

224

145

189

289

188

238

349

0.56

0.70

73

101

164

105

138

211

136

173

254

0.56

0.72

56

77

125

80

105

161

103

131

193

0.56

0.74

44

60

98

63

82

126

81

103

151

0.56

0.76

35

48

79

50

66

101

65

82

121

0.56

0.78

29

40

65

41

54

83

53

67

99

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

0.56

0.80

24

33

54

34

45

69

44

56

82

0.56

0.82

20

28

46

29

38

58

37

47

69

0.56

0.84

17

24

39

24

32

50

31

40

59

0.56

0.86

15

21

34

21

28

43

26

34

51

0.56

0.88

13

18

30

18

24

37

23

29

44

0.56

0.90

11

16

26

16

21

33

20

26

38

0.56

0.92

10

14

23

14

18

29

17

22

34

0.56

0.94

9

12

21

12

16

25

15

20

30

0.56

0.96

8

11

18

11

14

23

13

17

26

0.56

0.98

7

10

17

10

13

20

12

16

24

0.58

0.60

3627

4977

8084

5281

6887

10476

6880

8699

12686

0.58

0.62

903

1240

2015

1313

1714

2609

1710

2163

3157

0.58

0.64

400

549

893

580

758

1155

755

955

1396

0.58

0.66

224

307

500

324

424

646

421

534

781

0.58

0.68

142

196

319

206

269

411

267

339

496

0.58

0.70

98

135

221

142

186

284

184

233

342

0.58

0.72

72

99

161

103

135

207

133

170

249

0.58

0.74

55

75

123

78

103

157

101

128

189

0.58

0.76

43

59

97

61

80

123

79

100

148

0.58

0.78

34

47

78

49

64

99

63

80

119

0.58

0.80

28

39

64

40

53

81

51

65

97

0.58

0.82

23

32

53

33

44

67

42

54

80

0.58

0.84

20

27

45

28

37

57

35

45

68

0.58

0.86

17

23

39

24

31

48

30

39

58

0.58

0.88

15

20

33

20

27

42

26

33

49

0.58

0.90

13

18

29

17

23

36

22

28

43

0.58

0.92

11

15

26

15

20

32

19

25

37

0.58

0.94

10

14

23

13

18

28

17

22

33

0.58

0.96

9

12

20

12

16

25

15

19

29

0.58

0.98

8

11

18

10

14

22

13

17

26

0.60

0.62

3559

4884

7934

5180

6757

10280

6748

8533

12446

0.60

0.64

885

1216

1977

1287

1680

2558

1675

2120

3095

0.60

0.66

391

538

875

568

742

1131

738

935

1367

0.60

0.68

219

301

490

317

414

633

411

522

764

0.60

0.70

139

192

312

201

263

402

261

331

485

0.60

0.72

96

132

216

138

181

277

179

227

334

0.60

0.74

70

97

158

100

132

202

130

165

243

0.60

0.76

53

73

120

76

100

154

98

125

184

0.60

0.78

42

58

94

59

78

120

76

97

144

0.60

0.80

33

46

76

47

63

96

61

78

115

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

0.60

0.82

27

38

62

39

51

79

50

63

94

0.60

0.84

23

32

52

32

42

66

41

52

78

0.60

0.86

19

27

44

27

36

55

34

44

66

0.60

0.88

16

23

38

23

30

47

29

37

56

0.60

0.90

14

20

32

20

26

40

25

32

48

0.60

0.92

12

17

28

17

22

35

21

27

41

0.60

0.94

11

15

25

15

20

31

18

24

36

0.60

0.96

9

13

22

13

17

27

16

21

32

0.60

0.98

8

12

19

11

15

24

14

18

28

0.62

0.64

3476

4772

7753

5059

6600

10043

6589

8334

12158

0.62

0.66

864

1187

1931

1255

1639

2497

1633

2068

3020

0.62

0.68

382

525

854

553

723

1103

719

911

1333

0.62

0.70

213

293

478

308

404

616

400

508

744

0.62

0.72

135

187

305

195

256

392

253

322

472

0.62

0.74

93

129

210

134

176

270

174

221

325

0.62

0.76

68

94

154

97

128

197

126

160

236

0.62

0.78

52

71

117

74

97

149

95

121

179

0.62

0.80

40

56

92

57

76

117

74

94

140

0.62

0.82

32

45

74

46

60

93

59

75

112

0.62

0.84

26

37

60

37

49

76

48

61

91

0.62

0.86

22

31

50

31

41

63

39

50

75

0.62

0.88

19

26

43

26

34

53

33

42

63

0.62

0.90

16

22

36

22

29

45

28

36

54

0.62

0.92

14

19

31

19

25

39

24

31

46

0.62

0.94

12

16

27

16

22

34

20

26

40

0.62

0.96

10

14

24

14

19

30

18

23

35

0.62

0.98

9

13

21

12

16

26

15

20

30

0.64

0.66

3380

4640

7541

4918

6417

9767

6405

8102

11822

0.64

0.68

839

1153

1877

1219

1592

2427

1585

2008

2934

0.64

0.70

370

509

830

537

702

1071

697

884

1293

0.64

0.72

207

285

464

299

391

598

387

492

721

0.64

0.74

131

181

295

189

248

380

245

311

457

0.64

0.76

90

125

204

130

170

261

167

213

314

0.64

0.78

66

91

149

94

124

190

121

155

228

0.64

0.80

50

69

113

71

93

144

91

117

172

0.64

0.82

39

54

89

55

73

113

71

91

135

0.64

0.84

31

43

71

44

58

90

56

72

107

0.64

0.86

26

35

58

36

47

74

46

59

87

0.64

0.88

21

29

49

30

39

61

38

48

72

0.64

0.90

18

25

41

25

33

51

31

40

61

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

0.64

0.92

15

21

35

21

28

44

26

34

51

0.64

0.94

13

18

30

18

24

37

22

29

44

0.64

0.96

11

16

26

15

21

32

19

25

38

0.64

0.98

10

14

23

13

18

28

17

22

33

0.66

0.68

3271

4491

7299

4757

6209

9451

6195

7837

11438

0.66

0.70

811

1115

1815

1178

1539

2346

1531

1940

2836

0.66

0.72

358

492

802

518

677

1035

672

852

1249

0.66

0.74

199

275

448

288

377

577

373

474

695

0.66

0.76

126

174

285

182

239

366

235

299

440

0.66

0.78

87

120

197

125

164

252

161

205

302

0.66

0.80

63

87

143

90

119

183

116

148

219

0.66

0.82

48

66

109

68

90

138

87

112

166

0.66

0.84

37

52

85

53

70

108

68

87

129

0.66

0.86

30

42

69

42

56

86

54

69

103

0.66

0.88

24

34

56

34

45

71

43

56

84

0.66

0.90

20

28

47

28

37

58

36

46

69

0.66

0.92

17

24

39

23

31

49

30

38

58

0.66

0.94

14

20

34

20

27

42

25

32

49

0.66

0.96

12

17

29

17

23

36

21

28

42

0.66

0.98

11

15

25

15

20

31

18

24

36

0.68

0.70

3148

4323

7028

4578

5975

9098

5960

7541

11009

0.68

0.72

780

1073

1746

1131

1479

2256

1471

1864

2726

0.68

0.74

343

473

771

497

650

994

645

818

1199

0.68

0.76

191

264

431

276

361

554

357

454

667

0.68

0.78

121

167

274

174

228

351

225

286

422

0.68

0.80

83

115

189

119

157

241

153

196

289

0.68

0.82

60

84

137

86

113

175

111

141

209

0.68

0.84

46

63

104

65

85

132

83

106

158

0.68

0.86

36

49

82

50

66

103

64

82

123

0.68

0.88

28

40

66

40

53

82

51

65

98

0.68

0.90

23

32

54

32

43

67

41

53

79

0.68

0.92

19

27

45

27

35

56

34

44

66

0.68

0.94

16

23

38

22

30

47

28

36

55

0.68

0.96

14

19

32

19

25

40

23

30

46

0.68

0.98

12

16

28

16

21

34

20

26

40

0.70

0.72

3013

4138

6728

4380

5718

8708

5700

7214

10535

0.70

0.74

746

1026

1671

1081

1413

2157

1404

1780

2605

0.70

0.76

328

452

737

474

620

949

614

780

1144

0.70

0.78

182

252

411

263

344

528

340

432

636

0.70

0.80

115

159

261

165

217

334

213

272

401

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

0.70

0.82

79

109

180

113

149

229

145

186

275

0.70

0.84

57

80

131

81

108

166

105

134

199

0.70

0.86

43

60

99

61

81

126

78

100

150

0.70

0.88

34

47

78

47

63

98

60

78

116

0.70

0.90

27

38

62

38

50

78

48

62

92

0.70

0.92

22

31

51

30

41

63

38

50

75

0.70

0.94

18

25

42

25

33

52

31

41

62

0.70

0.96

15

21

36

21

28

44

26

34

51

0.70

0.98

13

18

30

17

23

37

22

28

43

0.72

0.74

2865

3936

6401

4164

5437

8282

5418

6859

10018

0.72

0.76

708

974

1588

1026

1342

2049

1332

1690

2474

0.72

0.78

311

429

700

449

588

901

582

739

1085

0.72

0.80

173

238

390

248

326

501

321

409

602

0.72

0.82

109

151

248

156

205

316

201

257

379

0.72

0.84

75

104

170

106

140

217

137

175

259

0.72

0.86

54

75

124

77

101

157

98

126

187

0.72

0.88

41

57

94

57

76

118

73

94

141

0.72

0.90

32

44

73

44

59

92

56

73

109

0.72

0.92

25

35

59

35

47

73

44

58

87

0.72

0.94

21

29

48

28

38

60

36

46

70

0.72

0.96

17

24

40

23

31

49

29

38

58

0.72

0.98

14

20

33

19

26

41

24

31

48

0.74

0.76

2706

3718

6049

3931

5134

7823

5114

6475

9461

0.74

0.78

668

919

1499

967

1265

1933

1255

1592

2333

0.74

0.80

293

404

660

422

554

848

547

695

1021

0.74

0.82

162

224

368

233

306

471

301

384

566

0.74

0.84

102

142

233

146

193

297

188

240

356

0.74

0.86

70

97

160

99

131

203

128

163

243

0.74

0.88

51

70

116

71

95

147

91

117

175

0.74

0.90

38

53

88

53

71

111

68

88

131

0.74

0.92

30

41

69

41

55

86

52

68

102

0.74

0.94

24

33

55

33

43

68

41

53

80

0.74

0.96

19

27

45

26

35

55

33

43

65

0.74

0.98

16

22

37

21

29

46

27

35

53

0.76

0.78

2536

3485

5671

3682

4810

7332

4789

6065

8865

0.76

0.80

625

860

1404

903

1183

1809

1172

1488

2182

0.76

0.82

274

377

618

394

517

793

509

648

954

0.76

0.84

151

209

344

217

285

439

280

357

527

0.76

0.86

95

132

217

136

179

277

174

223

331

0.76

0.88

65

90

149

92

122

189

118

151

225

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

0.76

0.90

47

65

108

66

88

136

84

108

162

0.76

0.92

35

49

82

49

65

102

62

81

121

0.76

0.94

27

38

64

38

51

79

48

62

94

0.76

0.96

22

30

51

30

40

63

37

49

74

0.76

0.98

18

25

41

24

32

51

30

39

60

0.78

0.80

2355

3238

5270

3418

4466

6811

4444

5630

8233

0.78

0.82

579

798

1303

837

1096

1677

1085

1378

2022

0.78

0.84

253

349

572

364

478

734

470

599

882

0.78

0.86

140

194

318

200

263

406

257

329

486

0.78

0.88

88

122

201

125

165

255

160

205

305

0.78

0.90

60

83

138

84

112

174

108

138

207

0.78

0.92

43

60

100

60

80

125

77

99

148

0.78

0.94

32

45

75

45

60

94

57

73

111

0.78

0.96

25

35

59

34

46

73

43

56

85

0.78

0.98

20

28

47

27

36

57

34

44

67

0.80

0.82

2165

2977

4848

3140

4105

6262

4081

5172

7566

0.80

0.84

531

732

1197

766

1005

1539

993

1262

1854

0.80

0.86

231

320

525

332

437

672

429

547

806

0.80

0.88

128

177

291

182

240

371

234

299

443

0.80

0.90

80

111

184

113

150

232

145

186

277

0.80

0.92

54

76

126

76

101

158

97

125

187

0.80

0.94

39

55

91

54

72

113

69

89

134

0.80

0.96

29

41

68

40

54

85

51

66

100

0.80

0.98

22

32

53

31

41

65

38

50

76

0.82

0.84

1966

2704

4406

2849

3726

5688

3702

4693

6870

0.82

0.86

481

664

1086

693

909

1394

897

1141

1678

0.82

0.88

209

289

475

299

394

607

385

492

728

0.82

0.90

115

159

263

163

216

334

209

268

399

0.82

0.92

72

100

166

101

134

209

129

166

248

0.82

0.94

49

68

113

68

90

141

86

111

167

0.82

0.96

35

49

81

48

64

101

61

79

119

0.82

0.98

26

36

61

35

48

75

44

58

88

0.84

0.86

1759

2420

3946

2547

3332

5090

3307

4195

6145

0.84

0.88

429

592

970

617

810

1244

797

1015

1496

0.84

0.90

186

257

424

265

349

540

341

436

646

0.84

0.92

102

141

234

144

190

296

184

236

353

0.84

0.94

63

88

147

89

118

184

113

145

219

0.84

0.96

43

60

100

59

79

124

75

97

147

0.84

0.98

30

43

72

42

56

89

52

68

104

0.86

0.88

1545

2127

3470

2234

2925

4472

2900

3680

5396

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

Power(1-β)=0.8

Power(1-β)=0.9

Power(1-β)=0.95

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

α=0.1

α=0.05

α=0.01

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

θ1

θ2

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

SSiz

0.86

0.90

375

519

851

538

708

1089

695

886

1307

0.86

0.92

162

225

370

230

304

470

295

378

562

0.86

0.94

88

123

204

124

165

257

158

204

305

0.86

0.96

54

76

127

76

101

159

96

124

188

0.86

0.98

36

51

86

50

67

107

63

82

125

0.88

0.90

1325

1826

2981

1913

2507

3838

2481

3152

4626

0.88

0.92

320

443

728

457

603

929

589

753

1114

0.88

0.94

137

191

316

194

257

399

248

319

476

0.88

0.96

74

104

173

103

138

216

131

170

256

0.88

0.98

45

64

108

63

84

133

79

103

156

0.90

0.92

1100

1518

2482

1586

2080

3189

2053

2612

3840

0.90

0.94

263

366

603

375

495

767

482

617

917

0.90

0.96

112

156

260

157

209

327

200

258

387

0.90

0.98

60

84

141

83

111

175

104

136

206

0.92

0.94

872

1205

1974

1253

1647

2530

1620

2064

3041

0.92

0.96

206

287

475

291

387

601

373

480

716

0.92

0.98

86

121

203

120

160

253

151

197

298

0.94

0.96

641

889

1461

917

1209

1865

1182

1510

2235

0.94

0.98

148

208

347

207

277

434

263

341

514

0.96

0.98

410

572

947

580

770

1197

742

955

1426

Hanley JA, McNeil BJ (1982) The meaning and use of the Area under a
receiver operating characteristic (ROC) curve. Radiology 143:29-36